Question
Fully simplify and write your answer in exponential form with positive exponents only. Example: 153\frac{1}{5^3}
5
3
1
not 5−35^{-3}5
−3
.
13−6⋅13−9=13^{-6}\cdot13^{-9}=13
−6
⋅13
−9
=
Answers
Answered by
GPT-4o mini
To simplify the expression \( 13^{-6} \cdot 13^{-9} \), we use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
So, we can add the exponents:
\[
13^{-6} \cdot 13^{-9} = 13^{-6 + (-9)} = 13^{-15}
\]
Now, to express this in exponential form with positive exponents, we write:
\[
13^{-15} = \frac{1}{13^{15}}
\]
Thus, the fully simplified answer is:
\[
\frac{1}{13^{15}}
\]
So, we can add the exponents:
\[
13^{-6} \cdot 13^{-9} = 13^{-6 + (-9)} = 13^{-15}
\]
Now, to express this in exponential form with positive exponents, we write:
\[
13^{-15} = \frac{1}{13^{15}}
\]
Thus, the fully simplified answer is:
\[
\frac{1}{13^{15}}
\]